Find the greatest common factor of $42, 28,$ and $70$.
Answer: The greatest common factor (GCF) is the largest number that is a factor of $42, 28,$ and $70$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}42 &=2\cdot3\cdot7\\\\\\\\ 28&=2\cdot2\cdot7\\\\\\\\ 70&=2\cdot5\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}42 &=2\cdot3\cdot7\\\\\\\\ 28&=2\cdot2\cdot7\\\\\\\\ 70&=2\cdot5\cdot7 \end{aligned}$ Each number shares the factor ${2}$ and ${7}$ so the GCF is $2\cdot7={14}$. The greatest common factor of $42, 28,$ and $70$ is $14$.